The bustle of the port is exhilarating: ship’s horns booming, sailors shouting, swarms of taxis on the quaysides. If a shot of adrenaline is required before any island-hopping adventure, Piraeus provides. I park myself in a kafeneio for an hour and drink in – with some bitter Greek coffee – the sheer excitement of travel in a place where millions of odysseys have begun.

When it comes to Greek island hopping, I really thought I’d missed the boat. “You should’ve seen it 30 years ago: it’s not the same now,” people had been telling me, along with tales of ferry chaos, rip-off prices and the blight of mass tourism. But now I’m in Piraeus, 10km south-west of central Athens, and it feels right. I’m going to what I hope are out-of-the-way islands – Ikaria, Kalymnos, Amorgos, Folegandros, Milos and Sifnos – each with a unique character. A great loop of seafaring will, over the next few weeks, take me across the Aegean Sea and back here.

But first I have a night in the port. I wander up to my hotel, The Alex, and discover that it has opened that very day. I am its first-ever guest. Konstantinos, the excited owner, is bent on proving that Piraeus is a worthy stopover and takes me on a whirlwind tour. Through him I see the magic of the place and the unbroken seafaring traditions that still pull the strings. We finish at sunset in his rooftop restaurant, with a stunning view across the port and all the way to the Parthenon, lit up on its distant hill.

Next morning I am at gate two on the quayside, where boarding is quick, efficient and not at all chaotic. Most people on the boat are going to Mykonos, but I am staying on to a lesser-known island: Ikaria, which has a reputation for its inhabitants living to fabulous old age. It was also, I read on the ferry deck, a place of exile for 16,000 communists after the second world war. Maybe I can weave these two themes together? As I tuck into a spinach and cheese pie, this foreknowledge gives me a sense of relief: the first chapter of my own odyssey is already shaping up.

Seven hours later I am sitting in a cafe in one of Ikaria’s two ports. Evdilos is a smartly painted village on a steep mountain slope covered in oaks and plumes of pink oleanders. My guide is Urania, local artist and travel agent, who walks me up through the village’s shady lanes and then back to a cafe by the sea.

“Ask me anything,” she says, ordering iced coffees and local cakes, “except – please – nothing about longevity.” It transpires that a couple of newspaper articles on the Ikarian age phenomenon triggered a deadly deluge of outsiders, all pestering anyone with half a wrinkle to cough up the secret of long life.

“At first we were all very polite,” Urania says. “I even arranged for one American channel to film a 97-year-old having breakfast, but when he rolled a cigarette, the director went crazy, shouting that it was all wrong. Now the old people refuse to tell their age.”

“I’m not interested in longevity,” I assure her, inwardly cursing.

“Good,” she says, cutting up the cakes for us to share. “The other subject to avoid is the communist stuff, but that wouldn’t interest you, would it?”

“Not at all.”

Later, Urania’s husband, Theo, gives me a lift to my hotel, the family-run Erofili up the coast in the village of Armenistis. I swim, then go for dinner at local restaurant Mary Mary, where Nikos, the owner, recommends the traditional Ikaria pie, filled with mixed greens, and soufiko.

“We eat lots of greens,” he tells me. “Soufiko is really just a mixture of what you have in the garden.” Nikos adds twists to such simple traditions, making superbly tasty dishes. His long-term ambition, however, belies this sophistication: he plans to retire to a smallholding up on the mountain. “I’ll keep chickens, grow vegetables and make cheese.”

Next day Urania and I drive up into the hills, and into the trees. Ikaria is a green island, and for centuries most of the population lived away from the coast. The old stone houses, some still inhabited, all face away from the sea, a relic of the time when pirates would roam the Aegean, looking for settlements to raid. In Christos Raches, the population went one step further, working their fields by night to avoid piratical attention. It still retains some of that nocturnal habit: its beautiful shady square is surrounded by tavernas, and at its liveliest after midnight. All around are oak forests and deep gorges dotted with waterfalls.

On a nearby hillside, local pharmacist Nikos Afianes is developing a vineyard and winery that also harks back to Ikaria’s past. “When I started, people told me that the soil was acidic, totally unsuitable for vines,” he says, “but I knew that in ancient times the island was famous for its wine.”

Nikos has dedicated a lifetime to researching this paradox, and rediscovered ancient Greek methods and materials. “We grow forgotten varieties, then ferment the wine in amphora buried in the earth using local strains of yeast.”

The result is organic wines that have won plaudits from both wine connoisseurs and archaeologists. We sit in Nikos’s vineyard, opening bottles. The white begleri is my favourite: its amber colour threatens sweetness, but the wine is as dry as flint, with a rolling symphony of flavours. I notice a clump of trees on a small hill and ask what it is.

“Our village cemetery,” says Nikos, offering to take me to see it. “It’s an interesting place.”

When we arrive, I immediately see why. Each gravestone is marked with dates, many with the age of the deceased. I read: 99, 88, 79, 88, 97, and then I stop. Born 1856. Died 1982. That makes 126.

Nikos is further down the line, shaking his head. “Only 70. Tragic. So young.” At the gate, he leaves me with two facts. “The soil stress on the vines means our wines have very high levels of resveratrol. Also, we use wild yeasts that yield beta-glucans.”

I go away and look these terms up. Resveratrol has been associated with longevity claims; and beta-glucans have been found to reduce cholesterol. Drinking Ikarian wine, it seems, does keep you young and fit.

That evening Urania and I finish up at a panegyri, a local celebration, held under huge ancient trees in the last golden rays of sunlight. We take trays the size of tables and load up with psiti (roast meat), prothesi (goat soup), horiatiki (salad) and longevity juice (wine). I’m introduced to the local sea captain and others. There are tourists here, but they’re heavily outnumbered by locals. Then the dancing starts: a line of people with arms over each other’s shoulders. The music gets louder. What is Urania saying? This wine is excellent! An old lady takes a turn. I lean forward but still can’t catch Urania’s words. She’s probably saying: “There’s Kaliopi. She’ll be 100 next week. Her mum will be down later.”

Next morning I walk into the bakery, where Giorgos, the owner, is wrapping small chocolate cakes in foil. I daren’t ask how old he is, but he tells me his love of history and politics started when he was a boy. “The men came back from the Greco-Turkish war in 1922 and sat around discussing what had happened.”

As he wraps cakes (and eats them), I calculate that he’s well over 90. Giorgios’s friend, who is of equal vintage, arrives, having walked several miles from his village. In his shirt pocket I spot a packet of tobacco. “What we have here,” they agree, “is solidarity. People help each other.”

I leave them chatting and drive to the far west of the island and the village of Karkinagri, with a sheltered harbour, perfect for swimming on a day when the wind is picking up. This area has many clumps of huge granite boulders, recently discovered by climbers. I explore them then, as the sun sinks, drive back up the coast to Nas, a village perched on a gorge above a wild stony beach. I eat fish at a taverna run by Thea . She was born in Michigan but returned to the ancestral island as soon as she could. “I just felt at home here. It’s about as different from the US as it’s possible to be. The food seems simple, but there may be six or seven wild ingredients in a dish. My husband collected that samphire.”

Our conversation leads, eventually, to the subject of long-lived Ikarians: how outsiders have studied the water, wine, olive oil, everything, trying to find a reason. For Thea the secret is in the local mindset. “My husband sums it up well: put life in your years and the years will come to you.”

At sunset I walk out on a high rocky headland to catch the last rays before the red disc sinks into the Aegean. A local man is staring out to sea. “Can you see?” he asks. I look where he is pointing, far out into the waves. Eventually I see it: a head bobbing up and down in the big rolling swells.

“Very danger,” he says. “Not good. Too much storm coming.”

We watch for a long time. Is it a suicide attempt? The swimmer is heading out from the cove towards the swell of purple twilight where the sun disappeared. I lose sight of the bobbing head and eventually clamber down to the beach, in time to see a naked woman emerge from the surf. She walks past me, totally unselfconscious, her face shining with excitement, and disappears into the gloaming. I have no idea if she is a local or visitor, but I’m sure that, in true Ikarian style, she has just put some life in her years.

• The trip was provided by Sunvil which has a week at Erofili Beach Hotel from £978pp B&B, including flights from the UK and transfers. Ferries were booked through ferries.gr (Piraeus to Ikaria €39.50 one-way). The Alex in Piraeus has doubles from €104 B&B. Airport transfers and accommodation were provided by Holiday Extras. More information from visitgreece.gr

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